where \(\vec{x}_k\)  is the field-center position of unit \(k\) , \(\sigma \)  is the
Gaussian scale constant, and \(A\)  and \(B\)  determine the strength of local
excitation vs. long-range inhibition, respectively. While this formulation
violates Dale's law, it illustrates the typical parsimony of attractor
map models [1]}. A network constructed from equations (REF ) and (REF )
supports self-organization of its activity into a singular, contiguous `bump'
that emerges as the network relaxes (Fig. REF B; [2]}).
The activity bump can then respond to input changes due to, e.g., movement
through the environment or internal processing. These conditions are
encapsulated within NeuroSwarms by analogizing (1) inter-agent visibility
(e.g., for a line-of-sight communication channel) to sparse, recurrent
network connectivity, and (2) a local kernel of inter-agent distances to
spatially-weighted synapses.
